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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E16">Th12</font></span>: <a NAME="T12"><span class="comment"><font color="firebrick">:: OSALG_4:12</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S</font> being   <a href="osalg_4.html#V2" title="OSALG_4:attr.2">locally_directed</a>  <a href="osalg_1.html#NM3" title="OSALG_1:NM.3">OrderSortedSign</a><br/>  for <font color="Olive" title="b2">U1</font> being   <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>  <a href="osalg_1.html#NM5" title="OSALG_1:NM.5">OSAlgebra</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b3">E</font> being   <a href="msualg_4.html#V2" title="MSUALG_4:attr.2">MSEquivalence-like</a>   <a href="osalg_4.html#M1" title="OSALG_4:mode.1">OrderSortedRelation</a> of <font color="Olive" title="b2">U1</font><br/>  for <font color="Olive" title="b4">s</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b5">x</font>, <font color="Olive" title="b6">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b2">U1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">s</font> holds <br/> (  <a href="osalg_4.html#K8" title="OSALG_4:func.8">OSClass</a> (<font color="Olive" title="b3">E</font>,<font color="Olive" title="b5">x</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="osalg_4.html#K8" title="OSALG_4:func.8">OSClass</a> (<font color="Olive" title="b3">E</font>,<font color="Olive" title="b6">y</font>) iff <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b5">x</font>,<font color="Olive" title="b6">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">E</font> <a href="msualg_4.html#K2" title="MSUALG_4:func.2">.</a> <font color="Olive" title="b4">s</font> )</div></div>
